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Question

For all complex numbers z1,z2, satisfying |z1|=12 and |z234i|=5, the minimum value of |z1z2| is

A
0
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B
2
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C
7
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D
17
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Solution

The correct option is A 2
C1(0,0) is center of bigger circle and C2(3,4) is center of smaller circle
C1B=r1=12 (radius of bigger circle)
C2A=r2=5 (radius of smaller circle)
C1C2=5, minimum value of |z1z2|=AB
now, C1C2+C2A+AB=C1BAB=1255=2

396896_263168_ans.PNG

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